MATHEMATICAL SCIENCES
Year:2010 | Volume:4 | Issue:2|Papers Count:8

In this paper, we giving certain properties of the commuting regular semigroups, we get significant results on semigroups. Our investigation involve certain interesting class of commuting regular semigroups.

In this paper, we prove the existence of common fixed point for mappings defined on complete metric spaces with w-distance p satisfying a general contractive inequality of type integral.

Many ranking methods have been proposed so far. The fuzzy number defuzzification method with continuous weighted quasi-arithmetic means was proposed by Yoshida in the domain (-¥,+¥). Recently in [22], the researcher used this method with the ordinary fuzzy set in a compact interval, that all the conclusions can be extended to the ordinary fuzzy set in [24] directly. This parameterized defuzzi cation can be used as a crisp approximation with respect to a fuzzy quan- tity. In this article, the researchers will use this defuzzification for ordering fuzzy numbers. This method can effectively rank various fuzzy numbers, their images and overcome the shortcomings of the previous techniques. The proposed model is studied for a broad class for fuzzy numbers. The calculation of this method is far simpler than the other approaches. This article also used some comparative examples to illustrate the advantage of the proposed method.

In this paper, we will present a new method for a Volterra integral equation with weakly singular kernel in the reproducing kernel space. Firstly the equation is transformed into a new equivalent equation. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation un(t) to the exact solution u (t) is obtained. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.

In this paper, an application of He’s homotopy perturbation method (HPM) is applied to solve a linear and non-linear diffusion-convection problem (NDCP).Diffusion-convection equations have special importance in engineering and sciences and constitute a good model for many systems in various fields. The nonhomogeneous equation is effectively solved by employing the phenomena of the self-cancelling noise terms whose sum vanishes in the limit. Some special cases of the equation are solved as examples to illustrate ability and reliability of the method. The results reveal that the He’s homotopy perturbation method is very effective and simple.

In this paper, we use Taylor series and Legendre functions of the second kind to remove singularity of the weakly singular Fredholm integral equations of the second kind with the kernel k (x, y) =1/(x-y)a 0<a<1. Legendre polynomials are used as a basis and some integrals that appear in this method are computed with Cauchy principal value sense without using any numerical quadrature. Three examples are given to show the efficiency of the method.

In this paper we consider the problem of the best approximation of a continuous multivariate function in two spaces L1 and L2 by optimization.

A new related fixed point theorem for three pairs of mappings on three complete metric spaces is obtained.